Problem: Rewrite as a simplified fraction. ${0.3\overline{45} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 345.4545...\\ 10x &= 3.4545...\end{align*}}$ Subtracting the two equations, we have: ${990x = 342}$ ${x = \dfrac{342}{990}} $ ${x = \dfrac{19}{55}} $